Key aides of embattled Egyptian President Hosni Mubarak quit the ruling National Democratic Party late on Saturday, abandoning the organization which the leader had presided over for nearly 30 years ago. As Egypt ended its 12th day of turmoil, state-run television announced that the party's Steering Committee of the General Secretariat  including Mubarak's son Gamal  was resigning from the party, meaning that none of them will succeed Mubarak, since Egypt's constitution requires that the country's president must be a party member.

In an effort to end the revolt and get the country back to normal, the head of the Egyptian Army's central command Gen. Hassan El-Rawani arrived in Tahrir Square  the revolt's iconic heart  early Saturday evening, and urged the crowds to leave the area, which is in downtown Cairo. That evoked chants of "We are not leaving, [Mubarak] is leaving," a familiar slogan of the nearly two-week uprising. The military left the square shortly after, abandoning their day-long efforts at negotiating an end to the protesters' occupation of the area, according to Al Jazeera. (See TIME's exclusive photos of the turmoil in Egypt.)

At the same time, reports circulated that the U.S. and other western powers were trying to fashion a compromise in which Mubarak's newly appointed vice-president Omar Suleiman would be de facto president as an interim step in easing the incumbent out.

But for now, Mubarak remains the fully empowered president. And he has vowed to stay until elections are held in September. Saturday's NDP announcement could signal the beginning of a speedier timetable than that, however, especially since U.S. officials have made it clear that the current upheaval is unsustainable. After dozens of people were killed in a 15-hour gun battle in downtown Cairo last Wednesday between Mubarak supporters and the protesters, President Barack Obama said that the transition needed to begin immediately.

The change in the ruling party's leading personalities is telling, too. The new secretary-general is Hossam Badrawi, regarded as being more liberal than his predecessor, Safwat El-Sherif, who has been a hugely powerful hard-liner for years, and who once ran Mubarak's propaganda machine as the Minister of Information. Now, Sherif's political career is all-but over. That is a measure of the revolt's seismic power, since it was Sherif who on Jan. 27 dismissed the mounting protests as trivial; one day later, protesters torched the hulking NDP headquarters, whose blackened structure now looms over Tahrir Square. (See video of the violent struggle for Tahrir Square.)

But the party resignations could well fail to stop the revolt, since the bottom-line demand for the tens of thousands of protesters in Tahrir Square is to oust Mubarak from power. That has not wavered an inch since the uprising exploded on Jan. 25, despite the fact that since then about 300 people have been killed and at least 600 people have been injured. The square has seen commemorations for the dead, including on Friday, when hundreds of thousands of people said the traditional Muslim prayer for the dead.

Although the crowds thinned out in the square on Saturday, several thousand people still arrived to hear political speeches, march and protest, and simply pass the day in an area which has captured the world's attention for nearly two weeks. There was no sign of the pro-Mubarak toughs who led assaults on the square mid-week; instead, the Special Forces controlled a tight cordon around the sole entrance to the square still open, creating a narrow funnel through which they could search each person, and check each identity. For the first time in a week, the October 6 Bridge which spans the Nile at Tahrir Square was open to traffic in both directions, and even buses were rumbling over it early Saturday morning.

With the change in atmosphere after days of spectacular battles, Egyptians turned Tahrir Square on Saturday into a family destination  a place to spend a weekend afternoon, despite the cold, drizzly weather. At the cordon leading into the square, Special Forces personnel hoisted small children over the razor-wire barricades, laughing and kissing them. (See how Egyptians are improvising security as lawlessness grows.)

Parents snapped photographs of their families, determined, they said, to be part of Egyptian history before the country moves on. "I want him to participate in the fight for democracy," says Ahmed Basoun, 36, who carried his one-year-old son Zizo on his shoulders. Zizo had a hand-written sign pinned to his woolen cap, reading, "we love Egypt." When I asked Basoun how Zizo would be able to remember the experience, he said, "my wife is photographing it and videotaping it, so when he grows up he will remember he was here." Nearby Wuda Noor carried his one-year-old daughter Fatima, who clutched a red balloon on which was written in pen: "Mubarak Finished."

With the economy losing tens of billions of dollars a week, there is a mounting sense among many people in the square  who include lawyers, businessman, and countless other professionals  that the crisis needs some quick closure. Much of Cairo  a city of 15 million  has ground to a standstill through two weeks of mammoth protests and gun battles. Stores are shut. Major roads are lined with military tanks and special-forces checkpoints. Tourism is non-existent, since most countries have advised their citizens to travel to Egypt only if necessary; in fact Tahrir Square is ringed by travel agents offering tours of the Pyramids and Valley of the Kings, and dominated by the huge, paralyzed construction site for the new Nile Ritz-Carlton Hotel, an absurd contrast to the drama unfolding in front of it.

As exhaustion sets in and the pressure grows to clear out the square and get back to business, protesters are anxious to make sure that their revolt does not end in a compromise, which leaves Mubarak in power for another seven months. "When Mubarak leaves, that is when we will leave," says Hazem Mounir, 26, a lawyer, who drove three hours from northern Egypt on Saturday to spend the night in Tahrir Square. And in the middle of the square on Saturday afternoon, graphic artist Hani Khaled, 23, arrived with a pot of black paint, kneeled down and painted a large sign on the asphalt reading: "Whoever leaves the square will be out of the revolution."